Consistency Conditions for Branes at Orbifold Singularities

TL;DR

This paper explores the necessary consistency conditions for placing branes at orbifold singularities, linking world-sheet tadpole cancellation with space-time anomaly cancellation, and provides explicit string theory constructions involving orbifolds and instantons.

Contribution

It introduces a detailed analysis of consistency conditions for branes at orbifold singularities, including new orientifold constructions with phases involving extra tensor multiplets.

Findings

Consistency conditions relate tadpole cancellation and anomaly cancellation.

Explicit constructions of orientifolds on $C^2/Z_M$ orbifolds.

Identification of phases with extra tensor multiplets from small SO(32) instantons.

Abstract

We discuss consistency conditions for branes at orbifold singularities. The conditions have a world-sheet interpretation in terms of tadpole cancellation and a space-time interpretation in terms of anomalies. As examples, we consider type II and type I branes on $C^2/Z_M$ orbifolds. We give orientifold constructions of phases of type I or heterotic string theory, involving branches with extra tensor multiplets, which arise when small SO(32) instantons sit on orbifold singularities.